ioo SCIENCE PROGRESS 



as to the enormous total mass of non-luminous matter in space 

 will be removed. It is perhaps necessary to recall that Bar- 

 nard's observations of dark patches in the sky seem con- 

 clusively to prove the existence of large masses of obscuring 

 matter in space, but we have no knowledge as to the distance 

 to which such matter extends. 



The Planets. — Some remarkable results in relation to the 

 orbital planes of the major planets are given by Prof. Plummer 

 in Monthly Notices, R.A.S., lxxvi. p. 387, March 191 6. The 

 three empirical laws which he has deduced are : 



(1) The poles of the orbital planes lie three by three on five 

 lines. Otherwise, the planes are concurrent, three by three. 



(2) The pole of each orbit, with the exception of Neptune, 

 lies on two of these five lines. 



(3) Each line contains the orbital poles of two adjacent 

 major planets. 



These relationships are governed by a curious law : 



(«S*) 



The figure shows a star pentagon, with two pairs of corners 

 joined. " The sides of the inner pentagon are numbered 

 alternately clockwise from 2 to 6 ; otherwise expressed, the 

 sides of the star pentagon are numbered consecutively. The 

 numbers 1 and 7 are placed on the additional sides to the left 

 and right alternately." Now let the numbers 1 to 8 inclusive 

 represent the planets Mercury, Venus, the Earth, Mars, Jupiter, 

 Saturn, Uranus, Neptune in order of distance from the Sun. 

 Then the corners of the figure indicate which sets of three orbital 

 planes are concurrent. 



